flow of the functionality

Author: curiecrypt

prover/docs/flow.md

@@ -0,0 +1,52 @@
+The flow of the functionality.
+
+## Registation
+* Each signer generates a key pair to be used for EdDSA.
+  * The secret key is an element of the scalar field $\mathbb{F}_r$ of the Jubjub elliptic curve.
+  * The public key is an affine point on Jubjub curve. It is of the form `(u, v)`. The coordinates are elements of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.
+* Signers share their public keys with the registration authority.
+* Registration authority collects the `u` coordinates of all the public keys in a list.
+* The aggregated public key is generated by hashing the list that includes `u` coordinates of all the public keys.
+  * The hash output is an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.
+
+## Signing
+Each signer generates a Schnorr signature and does the following:
+* Announcement:
+  * Generate a random scalar on the scalar field $\mathbb{F}_r$ of the Jubjub elliptic curve. 
+  * Multiply the random scalar with the generator. 
+    * The generator is an `ExtendedPoint` of the form `(U, V, Z, T1, T2)`. 
+    * So, we convert the multiplication result to an `AffinePoint` of the form `(u, v)`.
+* Challenge:
+  * Create a list including
+    * `x` coordinate of the announcement,
+    * `x` coordinate of the public key,
+    * The message.
+  * Note that, `x` coordinate mentioned above is equivalent to the `u` coordinate. Therefore, all the components of the list are elements of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.
+  * Generate the hash of the list.
+    * The hash output is an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.
+* Response:
+  * The response is the addition of the random scalar we used to generate the announcement, the secret key, and the challenge.
+  * Note that the random scalar and the secret key are the elements of $\mathbb{F}_r$, but the challenge is an element of the base field $\mathbb{F}_q$. We need to reduce the challenge, so that we can do the addition.
+    * Reduce the challenge to $\mathbb{F}_r$.
+    * Do the addition.
+* Output:
+  * Return the announcement which is an `AffinePoint` of the form `(u, v)` and the response which is a scalar, an element in $\mathbb{F}_r$.
+
+## Aggregation
+* The aggregator receives signatures sent by the signers and collects the threshold-many of them in a list as the aggregate signature.
+
+## Verification
+* The verifier receives:
+  * signatures: Schnorr signatures including an `AffinePoint` of the form `(u, v)` and the response which is a scalar, an element in $\mathbb{F}_r$.
+  * pks: The list of all public keys. The public keya are affine points of the form `(u, v)` on Jubjub curve. 
+  * commited_pks: The aggregated public key, an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.
+  * msg: The message is an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.
+  * threshold: The threshold is in the form of an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.
+* Collects the `x` coordinates of the all public keys in a list and generates a hash of the list.
+  * The hash output is an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.
+* Checks whether the hash output is equal to the committed_pks.
+* Iterates though the signatures and the public keys and verifies each signature with respect to the message and the corresponding public key.
+* Counts the number of valid signatures.
+* Verifier accepts if 
+  * The list of public keys produce the committed_pks and
+  * There are threshold-many valid signatures.

prover/docs/intro.md

@@ -59,4 +59,4 @@ This section includes the basic primitives of elliptic curve cryptography requir
   * We give a brief introduction to [ATMS][crate::docs::atms#atms-ad-hoc-threshold-multi-signatures] and explained the [SNARK-based ATMS with Schnorr setup][crate::docs::atms#snark-based-atms-with-schnorr-setup].
 * **Rescue sponge:** [Rescue][crate::docs::rescue]
 * **Encoding and I/O:** [Encoding and I/O][crate::docs::encoding_io]
-* **Flow:** 
+* **Flow:** [Flow][crate::docs::flow]

prover/src/docs.rs

@@ -13,4 +13,7 @@ pub mod schnorr {}
 pub mod rescue {}
 
 #[doc = include_str!("../docs/docs-encoding-io.md")]
-pub mod encoding_io {}
+pub mod encoding_io {}
+
+#[doc = include_str!("../docs/flow.md")]
+pub mod flow {}